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On methods for continuous systems with quadratic and cubic nonlinearities (1992)

Nayfeh, A. H. ; Nayfeh, J. F. ; Mook, D. T.

Springer

Nonlinear dynamics 3 (1992), S. 145-162

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ISSN: 1573-269X

Keywords: Averaged Lagrangian ; valve ; resonances ; Galerkin procedure

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Methods for determining the response of continuous systems with quadratic and cubic nonlinearities are discussed. We show by means of a simple example that perturbation and computational methods based on first discretizing the systems may lead to erroncous results whereas perturbation methods that attack directly the nonlinear partial-differential equations and boundary conditions avoid the pitfalls associated with the analysis of the discretized systems. We describe a perturbation technique that applies either the method of multiple scales or the method of averaging to the Lagrangian of the system rather than the partial-differential equations and boundary conditions.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00118990

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